equation of motion

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equation of motion

[i′kwā·zhən əv ′mō·shən]
(fluid mechanics)
One of a set of hydrodynamical equations representing the application of Newton's second law of motion to a fluid system; the total acceleration on an individual fluid particle is equated to the sum of the forces acting on the particle within the fluid.
(mechanics)
Equation which specifies the coordinates of particles as functions of time.
A differential equation, or one of several such equations, from which the coordinates of particles as functions of time can be obtained if the initial positions and velocities of the particles are known.
(quantum mechanics)
A differential equation which enables one to predict the statistical distribution of the results of any measurement upon a system at any time if the initial dynamical state of the system is known.
References in periodicals archive ?
We can see that without it we would get inconsistent equations of motion for [psi] and [[psi].
The problem is that (1), together with the linearity of the equations of motion entails that:
The pre-mentioned differential formulation of the equations of motion is equivalent to integral formulation, which requires the application of Lagrange's equation of motion.
The equations of motion developed for this model (with sample contact) can be solved to yield an equation for the contact stiffness, S, that is a function of previously calibrated instrument parameters (i.
Much later in this paper, we observe (albeit with important reservations) that a mechanical process can be shown to be reversible if the equations of motion are invariant--but the argument that shows this requires that the system under consideration be deterministic, and that is why the title of this paper promises that determinism will become involved here.
However, Scott Tremaine of the Canadian Institute for Theoretical Astrophysics (CITA) at the University of Toronto and his collaborators, working independently of Laskar, used computers to solve directly the equations of motion for the solar system's planets, tracking the evolution of their orbits over a 6-million-year period.
The Newton equations of motion will be transformed to Lagrange equation as a bridge to analytical dynamics.
Brizard presents students, academics, and researchers with the second edition of his comprehensive introduction to Langrangian mechanics, the history of the Langrangian method, FermatEs Principle of Least Time, and the mathematical principles of several mathematical predecessors of HamiltonEs Principle of Least Action and the Euler-Lagrange equations of motion.
The differential equations of motion of the mass particles are requested for each interval of motion from impact to impact, from collision to collision, and the interval of motion when the friction force direction alternation appears associated with the direction alternation of angular velocity of motion of a mass particle, and also velocity alternation as a consequence of the mass particle impact into the angular elongation limiter and mutual impact of the mass particles.
2] to the expressions of instantaneous mechanical energy, spectral shift and equations of motion for test particles and photons in combined spherically symmetric gravitational and electric field.
Like earlier editions (the first was published in 1990), this text follows a logical order of analysis: mathematical modeling, formulation of the equations of motion, and solution of the equations.